Regularity of the -Neumann problem
We prove a theorem on the boundary regularity of a purely p-dimensional complex subvariety of a relatively compact, strictly pseudoconvex domain in a Stein manifold. Some applications describing the structure of the polynomial hull of closed curves in Cn are also given.
Neither real analytic sets nor the images of real or complex analytic mappings are, in general, coherent. Let be a morphism of real analytic spaces, and let be a homomorphism of coherent modules over the induced ring homomorphism . We conjecture that, despite the failure of coherence, certain natural discrete invariants of the modules of formal relations , , are upper semi-continuous in the analytic Zariski topology of . We prove semicontinuity in many cases (e.g. in the algebraic category)....
This is a sequel to “Relations among analytic functions I”, Ann. Inst. Fourier, 37, fasc. 1, [pp. 187-239]. We reduce to semicontinuity of local invariants the problem of finding solutions to systems of equations involving division and composition by analytic functions. We prove semicontinuity in several general cases : in the algebraic category, for “regular” mappings, and for module homomorphisms over a finite mapping.
Dans cet article, nous montrons que la notion analytique d’exposants développée par Levelt pour les systèmes différentiels linéaires en une singularité régulière s’interprète algébriquement en termes d’invariants de réseaux, relatifs à un réseau stable maximal que nous appelons « réseau de Levelt ». Nous obtenons en particulier un encadrement pour la somme des exposants des systèmes n’ayant que des singularités régulières sur ).
We study the relative discrete series of the -space of the sections of a line bundle over a bounded symmetric domain. We prove that all the discrete series appear as irreducible submodules of the tensor product of a holomorphic discrete series with a finite dimensional representation.
Given a real analytic manifold Y, denote by the associated subanalytic site. Now consider a product Y = X × S. We construct the endofunctor on the category of sheaves on and study its properties. Roughly speaking, is a sheaf on . As an application, one can now define sheaves of functions on Y which are tempered or Whitney in the relative sense, that is, only with respect to X.